Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in PYTHON3):

Solution:
import copy

n = int(input())
data = list(map(int, input().split()))
data.sort()

data1 = copy.copy(data)
A = data1.pop()
B = data1.pop()
n_1 = n-2

min = 100000000
for i in range(n_1 - 1) :
    if data1[i+1] - data1[i] < min :
        min = data1[i+1] - data1[i]
        C = data1[i+1]
        D = data1[i]

ans_1 = (A+B) / (C-D)

data2 = copy.copy(data)

min = 100000000
for i in range(n - 1) :
    if data2[i+1] - data2[i] < min :
        min = data2[i+1] - data2[i]
        C = data2[i+1]
        D = data2[i]

data2.remove(C)
data2.remove(D)
A = data2.pop()
B = data2.pop()

ans_2 = (A+B) / (C-D)
print(max(ans_1, ans_2))